in both cases vs in either case

Some examples from the web:

• Natural treatment for hypothyroidism can be required in both cases.
• The files get deleted permanently in both cases.
• This is true in both cases of online and offline DM.
• 1490-1562) seems to be the stylistic model in both cases.
• The Commission is currently monitoring the situation in both cases.
• And in both cases, it has produced astonishing variety.
• 'The suspect in both cases is Mark White.
• Weapon in both cases is a 12-gauge shotgun.
• And in both cases, The Voice had leverage.
• Reasons for the rejections in both cases were seen in the worsened economic situation.
• The term of office in both cases is four years.
• There are exceptions in both cases, however.
• Suspect three delivered the killing blow in both cases.
• The same kinds of services are performed in both cases.
• I was wrong in both cases.
• Assessments of the responses provided by customers indicate general satisfaction in both cases.
• Behind the flash in both cases is a certain substance.
• But in both cases you will need to know some of the characteristics of the trench.
• Note that in both cases minimum required must be guaranteed.
• Well made but much simpler in both cases

Some examples from the web:

• Apr 22, 2015 ... "Any", as you seem to recognize, does give an implication that there are multiple options. However, "in either case" is used less frequently ...
• Today I met a new phrase, "in either case", but I am not sure if it makes sense to you. Got a minute? Take a look at this sentence I made.
• Sep 14, 2011 ... Hi, Question: Why does the sentence use in either case not in both cases? Sentence: The deaths of two young men whose bodies were found ...
• The hypothermia it induces in non-febrile mice, therefore, is due to another mechanism. PGHS-1b is not involved in either case. Go to: ...
• Jan 6, 2020 ... Synonym for In any cases in any case = three or more possible choices in either case = two possible choices We could go to Paris, ...